Solving Systems

This system has _____ solutions

• no

• 1

• 2

• Infinitely many

What is the solution?
(Hint:  Both lines are graphed over each other)

• One Solution

• No solution

• Infinitely Many Solutions

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38
  2s + 3c = 52

• 3s + 1c = 38
  3s + 2c = 52

• s + c = 38
  s + c = 52

• 3s + 3c = 38
  1s + 2c = 52

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all.  Upon completing the job he counted out the coins and it came to $6.60.  Which system of equations could be used to find the exact number of dimes and nickels? 

• d + n = 6.60
  .10d + .05n = 80

• d + n = 80
  d + n = 6.60

• d + n = 80
  .10d + .05n = 6.60

• d + n = 80
  .05d + .10n = 6.60

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

• t + n = 54
  t = 3n + 8

• t + n = 54
  n = 3t + 8

• t + n = 54
  t = 3n - 8

• t + n = 8
  t = 3n + 54

^{What is the solution?} 

• 1

• -2

• (1, 2)

• (1, -1)

How many solutions will this system have? 

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

7x - 5y = -24
-9x + 5y = 18

• (3, 9)

• (-3, -5/3)

• (3, 11)

• (3, -11)

What is the solution to this system?

• (1, -1)

• (-1, 1)

• (0, -2)

• (2, 0)

If a system of linear equations has infinitely many solutions, what does this mean about the two lines? 

• Intersecting lines

• Same line

• Parallel lines